I've tried several browsers on both Windows 10 and Mac OS 10.13.6 - Chrome, Firefox, Edge, Safari, and on three different networks (two at work and one at home). So, I'm assuming it's a server-side issue, either with file permissions, or the PHP version, or whatever.
I can go into the new category screen, and enter the data (category name, date, etc), and when I press the add key, this is when I get the 403 error message.
If you'd like, I can pm you the url, username and password for the admin area and let you try?